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          作业5
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            @
            
              Lindixuan
            
            · Tuesday, Oct 6, 2020
            · 2 minute read
            · Update at Oct 6, 2020
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      <article style="margin-top: 2rem;"><h2 id="1-give-the-three-representations-of-an-and-gate-and-say-in-your-words-what-and-means">1) Give the three representations of an AND gate and say in your words what AND means.</h2>
<p><img src="https://lindixuan.gitee.io/post/assets/%E4%BD%9C%E4%B8%9A5/andGate.png" alt="and"><br>
与门（AND gate）是一种基本逻辑门电路，可以有多个输入端，有一个输出端。当所有输入端都为1（高电平）时，输出1（高电平），否则输出0（低电平）。</p>
<h2 id="2-give-the-three-representations-of-an-xor-gate-and-say-in-your-words-what-xor-means">2) Give the three representations of an XOR gate and say in your words what XOR means</h2>
<p><img src="https://lindixuan.gitee.io/post/assets/%E4%BD%9C%E4%B8%9A5/XorGate.png" alt="xor"><br>
异或门（XOR gate）是数字电路中实现逻辑异或的逻辑门。当两个输入电平相同（均为0或1）时，输出1（高电平），当两个输入电平相异（一个为0一个为1）时，输出0（低电平）。</p>
<h2 id="3-draw-a-circuit-diagram-corresponding-to-the-following-boolean-expression-a--bb--c">3) Draw a circuit diagram corresponding to the following Boolean expression: (A + B)(B + C)</h2>
<p><img src="https://lindixuan.gitee.io/post/assets/%E4%BD%9C%E4%B8%9A5/3.png" alt="3"></p>
<h2 id="4-show-the-behavior-of-the-following-circuit-with-a-truth-table">4) Show the behavior of the following circuit with a truth table:</h2>
<p><img src="https://lindixuan.gitee.io/post/assets/%E4%BD%9C%E4%B8%9A5/4ti.png" alt="4t"></p>
<p><img src="https://lindixuan.gitee.io/post/assets/%E4%BD%9C%E4%B8%9A5/4table.png" alt="4tab"></p>
<h2 id="5-what-is-circuit-equivalence-use-truth-table-to-prove-the-following-formula">5) What is circuit equivalence? Use truth table to prove the following formula.</h2>
<h2 id="ab--a--b">(AB)’ = A’ + B’</h2>
<p>等效电路（circuit equivalence），所谓等效，是指将电路中某一部分比较复杂的结构用一比较简单的结构替代，替代之后的电路与原电路对未变换的部分（或称外部电路）保持相同的作用效果。<br>
∵(AB)’ ，A’ + B’的真值表均为：</p>
<p><img src="https://lindixuan.gitee.io/post/assets/%E4%BD%9C%E4%B8%9A5/5table.png" alt="5tab"><br>
∴(AB)’ = A’ + B’</p>
<h2 id="6-there-are-eight-1bit-full-adder-integrated-circuits-combine-them-to-8bit-adder-circuit-using-the-following-box-diagram">6) There are eight 1bit full adder integrated circuits. Combine them to 8bit adder circuit using the following box diagram.</h2>
<p><img src="https://lindixuan.gitee.io/post/assets/%E4%BD%9C%E4%B8%9A5/8%E4%BD%8D%E5%8A%A0%E6%B3%95.png" alt="adder"></p>
<h2 id="7-logical-binary-operations-can-be-used-to-modify-bit-pattern-such-asx8x7x6x5x4x3x2x12-and-000011112--0000x4x3x2x12-we-called-that-000011112-is-a-mask-which-only-makes-low-4-bits-to-work-fill-the-follow-expression">7) Logical binary operations can be used to modify bit pattern. Such as(X8X7X6X5X4X3X2X1)2 and (00001111)2 = (0000X4X3X2X1)2 We called that (00001111)2 is a mask which only makes low 4 bits to work. Fill the follow expression</h2>
<p>(1) (X8X7X6X5X4X3X2X1)2 or (00001111)2 = (X8X7X6X51111)2</p>
<p>(2) (X8X7X6X5X4X3X2X1)2
xor (00001111)2 = (X8X7X6X5X4&rsquo;X3&rsquo;X2&rsquo;X1&rsquo; )2</p>
<p>(3) ((X8X7X6X5X4X3X2X1
)2 and (11110000)2 )<br>
or (not (X8X7X6X5X4X3X2X1)2and(00001111)2) = (11111111 )2</p>
<h1 id="维基百科解释名词">维基百科解释名词</h1>
<h2 id="logic-gate">Logic gate</h2>
<blockquote>
<p>A logic gate is an idealized or physical electronic device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device (see Ideal and real op-amps for comparison).</p>
</blockquote>
<h2 id="boolean-algebra">Boolean algebra</h2>
<blockquote>
<p>In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0, respectively. Instead of elementary algebra, where the values of the variables are numbers and the prime operations are addition and multiplication, the main operations of Boolean algebra are the conjunction (and) denoted as ∧, the disjunction (or) denoted as ∨, and the negation (not) denoted as ¬. It is thus a formalism for describing logical operations, in the same way that elementary algebra describes numerical operations.</p>
</blockquote>
<h2 id="flip-flop-的中文翻译是">Flip-flop 的中文翻译是</h2>
<blockquote>
<p>触发器、触发电路。</p>
</blockquote>
<h2 id="how-many-bits-information-does-a-sr-latch-store">How many bits information does a SR latch store?</h2>
<blockquote>
<p>2 bits</p>
</blockquote></article>
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